Spherically curved plotting body and compass for use therewith



D. A. M MILLEN ET AL SPHERICALLY CURVED PLOTTING BODY AND COMPASS FORUSE THEREIW ITH Dec. 2, 1952 4 Sheeis-Sheet 1 Original Filed Aug. 4,1942 l lllllm INVENTQI g I BY Xx? 2 iillll Hm.

D. A. MCMILLEN ET AL Dec. 2, 1952 SPHERICALLY CURVED PLOTTING BODY ANDCOMPASS FOR USE THEREWITH 4 Sheets-Sheet 2 Driginal Filed Aug. 4, 1942Dec. 2, 1952 D. A. MOMILLEN ET AL 9,7

SPHERICALLY CURVED PLOTTING BODY AND COMPASS FOR USE THEREWITH OriginalFiled Aug 4, 1942 4 Sheets-Sheet 3 Dec. 2, 1952' D. A. MOMILLEN ETAL2,619,7

SPHERICALLY CURVED PLOTTING BODY AND COMPASS FOR USE THER EWITH OriginalFiled Aug. 4, 1942 4 Sheets-Sheet 4 WRNEY Patented Dec. 2, 1952''SPHERICALLY EURVED PLO-THING BODY AND COMPAS'S'FGR USE'THEREWITH.

Drury A. McMillenand Anton Stuxberg, Sao Paulo, Brazil Originalapplication August 4, 1942, Serial No. 453,608. Divided .and thisapplication May 1 2,

19:45,, :Serial 9N0. 5.93;458.

iClaims. 1

This application is a division of my copendr ing application, nowabandoned, .Serial. .No. 453,608; filed August 4, 71942.

The present invention relates to celestial navigatiornthat is, thedetermination of position on the earthfs surface by the aid .of theobservation of one or more celestial bodies.

Modern celestial navigation has been developed over a period of abouttwo centuries, starting with the invention of the sextant, the marine'chronom'e'ter "and the printing of the "first nautical almanac, but asuntil very recently developed has been directed toward the determinationof "position of relatively slow moving'bodies such as ships. As thusdeveloped, celestial navigation has involved complex and time. consumingcalculations requiring among otherthings the determination by deadreckoning of an assumed position as a starting point forcalculations-andthe mathematical solution .of the socalledsp'hericaltriangle. This procedure, while of practical utility'in'the hands ofa-skil'led navigator for determining the position of a ship; is whollyinadequate, because of the time element involved, for determining theposition of an "aircraftythe speed-of which, coupled'with unknown winddrift and other variables affecting aircraft flight, would in manyinstancesrenderdmpossible the determination bydead reckoning of anassumed position with sufficient accuracy to be usable and which wouldrender the computed result of such observations useless.

=Owing to the rapid development ofai-rcraft capable ofsustained fiight'over long distances In Ganada June 9,,

and the f act that because of the altitude at which such craft can beflown, observation of celestial bodies is usually readily effected, muchattention has 'in'recent years been given "to the problem of simplifyingthe earlier methods ofcelestial navigation in order to reduce the timeelement required to determinea position from a given set ofobservations. Proposals heretofore made' have, however, been in the maindirected toward attempts to speed up existing methods of chart-- ingcourses by providing tables giving in very complete and minute detailthe data covering the positions 0f the celestial bodies considereduseful for the purposes of celestial navigation and tables of logarithmsand other mathematical (tables and charts. Such very complete data isextremely voluminous :and while permitting certain short cuts-to betaken does not eliminate the :necessity for the utilization :of a deadreckoned .position as :a :starting point, :the computation and transferof :data from :a :system :of

spherical coordinates to a :distorted two ldimensional chart and otherfactors which are not only time consuming but which introduce errors ofinadmissible magnitude. Moreover, even with the most simplified ofsystems heretofore proposed, long and thoroughmathematical andnavigational training are required :before they can be intelligentlyused without ,risk of a serious error in result, particularly when .itisessential that the result be obtained with the utmost speed.

It is therefore a general object of the present invention to providenovel means whereby positions on the earths surface may be determinedfrom celestial observations with suflicient -=ra pidity, certainty andaccuracy to render celestial navigation wholly practical as a method fordetermining the position of bodies travel-Ting as rapidly as "high speedaircraft. A further generalo'bject of the invention is the provision ofnovel celestial navigational means which are reduced to such simple andreadily comprehensible nature as to be practically usable by one havingonly relatively rudimentary mathematical training and with little if anyprevious navigational training. A further general objectof the inventionis the provision of improved means of the above described kind whichshall be usable either by night or by day as conditions'may require.

The above general'objects, and otheriand more detailed objects whichwill become apparent as this description proceeds, are obtained inaccordance with our invention by a system based upon graphical solutionof the problems of sph-erical trigonometry required to be solved "inorder to translate celestial observations into terms of the geographicalposition of the observer. Stated in another way our inventioninvolves-what may be termed spherographical methods which contemplatethe direct transfer of celestial observational data to and the plottingthereof upon a spherically curved body representative of the surface ofthe earth or a portion thereof "andhaving a predetermined known scalerelationship to the earth's dimensions. 'Forpurposes of convenience suchbody will be referred to "herein as a plotting body.

.In order to determine positions ,from celestial observations .by theaid of .such a plotting body various different specific procedures maybe followed, the nature of which will ,be dictated by the conditionsunder which :the projected flight lislto best be had to the ensuingportion of this specification taken in conjunction with the accompanying drawings forming a part hereof and illustrative of the instrumentsto be employed and the manner of their utilization.

In the drawings:

Figs. 1 and 2 are top plan and elevation views, respectively, of oneform of plotting body suitable for use in practicing the invention, Fig.2 showing in addition an arcuate rule or a compass intended to be usedin conjunction with the plotting body;

Fig. 3 is a view on enlarged scale of a part of the structure shownin'Figs. 1 and 2;

Figs. 4 and 5 are end and fragmentary side views, respectively, onenlarged scale, of the arcuate rule shown in Fig. 2;

Fig. 6 is a fragmentary view on enlarged scale of another portion of thearcuate rule shown in Fig. 2, showing a vernier slide and scaletherefor;

Fig. 7 is a section taken at right angles to Fig. 6;

'Fig. 8 is a transverse section of still another portion of the arcuaterule shown in Fig. 2;

Fig. 9 is anelevation showing a great circle rule intended for use inconjunction with the plotting body of Figs. 1' and 2;

Fig. 10 is a top plan view of the rule shown in Fig. 9;

Fig. 11 is a transverse section of the rule shown in Fig. 9; v

Fig. 12 is a top plan view of a protractor intended for use with theplotting body shown in Figs. 1 and 2;

Fig. 13 is a side elevation of the protractor shown in Fig. 2;

Fig. 14 is a top plan view of a measuring instrument intended for usewith the plotting body of Figs. 1 and 2;

Fig. 15 is a side view of the instrument shown in Fig. 14;

Fig. 16 is an elevation of a shield usable with the plotting body shownin Figs. 1 and 2;

Fig. 17 is a side view of the shield shown in Fig. 16;.

Fig. 18 is a diagram showing the use of a spherical plotting body foreffecting one kind of navigation by the present invention. Y

Referring now more particularly to Figs. 1 through 17, we will. firstdescribe suitable examples of the instrumentalities required orconveniently usable in the practice of our invention, thereafterdescribing the methods of their use to secure the desired results.

In Figs. 1 and 2 there is shown at I0 a plot-ting body having aspherically curved surface the radius of which bears a predeterminedscale relationship to the radius of the earth. For reasons hereinaftermore fully appearing, we prefer to make this body with a surface havinga radius of 171.88 millimeters, this radius corresponding to a scale of3 millimeters to 1 of arc of a great circle on the surface of the earth.In the example shown, the plotting body provides slightly more than ahemisphere, mounted for convenience on a base l2, but in so far as theexercise of the present invention 'is concerned, the surface of theplotting body may constitute a lesser portion of a sphere or mayconstitute a complete sphere or globe;

Choice of the extent of the surface area provided by the plotting bodywill be determined largely by its intended use. If courses which are tobe plotted thereon lie within one hemisphere of the globeth-e form ofbody illustrated herein may 4 be most convenient. If intended for use innavigation involving courses lying in more extended areas the fullglobular form will ordinarily be most convenient. v

Advantageously, but not necessarily, the surface of the plotting body I0 has permanently marked thereon an equator line I l and a Greenwichmeridian line is, the equator line having associated therewith a scaleindicating degrees of longitude.

A rigid arcuate member, which in the example shown is a half hoop andwhich in case of the use of a full globular plotting body may be in theform of a complete hoop, is pivotally mounted as at It and Hi to haverelative pivotal movement with respect to the surface of the plottingbody, the pivot points being coincident with a diameter of the body I0.For convenience this member may be termed a meridian rule. If the bodyIn provides a complete globular surface, thus making a base of the typeherein illustrated inconvenient to use, the globular body may be mountedon a pedestal of small diameter or carried from a suitable base by ayoke attached at the pivot points of the meridian rule, or the mountingmay be attached to the meridian rule. leaving the globe free to revolveabout the axis determined by the pivot points. The pivot mountings forthe meridian rule are conveniently provided with thumb screws 2e and 22usable to clamp the meridian rule and plotting body in any desiredposition relative to each other.

The form of the member [4 is such that one side 24 thereof will lieexactly in a diametral plane passing through the pivot points l6 and I8,this side being planar and further preferably having its inner edgecurved to a radius only enough greater than the radius of the surface ofthe plotting body to provide necessary clearance. To aid in this, theradially inner surface of the member I4 may if desired be made concavelyspherically curved to approximately the radius of body In.

The side 24 of member 14 is preferably provided with a degree scale,showing degrees of are numbered on each side away from a zero marklocated midway between the pivot points.

The side 26 of the meridian rule, which obviously cannot lie on adiameter, is advantageous- 1y made of waved or other non-planarconfiguration to insure it not being mistakenly used by an operator forthe side 24 which corresponds In the embodiment to a true meridian line.shown, the meridian rule is provided with a small manipulating handle 28and the plotting body is conveniently provided with small diametricallyopposed stops 3i! and 32 to limit the arc of travel of the pivoted rule.

The member H5 is provided with a marking or scribing slide 34 arrangedto engage and slide along suitable guide grooves 36 in the member l4 andbeing provided with a clamping bolt and screw 38, the head of the boltsliding in a suitable undercut groove in the member I. The slide 34carries a marking element 40, which may be a pen, pencil or scribingpoint, suitably clamped in position by the clamping screw 42.

Referring now more particularly to Figs. 2 and 4 to 8, there is shown anarcuate rule indicated stud 48, preferably provided at its lower endwith a socket retaining a ball 50 providing a foot.

At its opposite end member 46 carries an adjustably mounted markingelement such as a pencil or scribe-r .52, the extent of the radialprojection of which from the member 46 is governed by the clamping screw54. The marking element is mounted in a carrier 56 having a pivot pin 58passing through a suitable hole in the member 46 and secured in place bymeans of a thumb nut 60.. At its outer end the carrier '6 is slotte'd asat 62 to provide a forked end through which .a thumb screw 64 extendsinto the member 46. Clearance is provided between the several parts sothat the point of the marking element may be adjusted longitudinally aswell as radially with respect to the member 4'6, being held in desiredadjusted position by the several thumb screws. At its outer edge themember 46 is provided with anarcuate degree scale 56. The innerand outerfaces of member 46 are provided with grooves 68 and 10, respectively,and one side faceis provided with a dovetail groove 12. A slide member14 is mounted so as to slide in the grooves 68 and and carries aclamping bolt having atapered head 13 located in the dovetail groove 12.A thumb nut 80 on the clamping bolt 16 enables the slide 14 to be fixedin any desired position lengthwise of the member 46.

The slide 14 carries a sharp scribing point 82 held by the clampingthumb screw '84 and the outer face of the slide M advantageously,although not necessarily, carries a Vernier scale 86. As will beevident, the sharp point 82 may be used as .a center engaging thesurf-ace of the plotting body, about which the body member is swung toproduce circular arcs on the plotting body by the action of the pencilor scribing element 52.

Referring more particularly to Fig. .2, the following characteristics ofthe rule or compass just described are to be noted. The curvature of themember is such that the center about which the arc of the scale 66 isstruck coincides with the center of the plotting body when the rule isplaced on the plotting surface in the manner shown in Fig. 2. This is ofcourse readily accomplished by suitable adjustment of the position ofthe bearing foot and the scribing point 82, both of these elements beingmounted to move along radial lines. Regardless of whether or not aVernier scale 86 is employed, the slide M is provided with :a zero markfor use with the scale 66, which mark is radially coincident with theaxis of the scribing point 82 carried by the slide.

Referring now to Figs. 9 to 11 inclusive there is shown a great circlerule for use with the plotting body Hi. This rule comprises an arcuatelycurved member indicated generally at 88 having a concave sphericallycurved surface 90, the radius of which is the same at the radius of thesurface of the plotting body Iii. A sharp edge 92 of the surface 91)coincides with the line of intersection between the surface 90 of therule and a diametral plane passing through the center about whichtheradius of the surface 98 is struck. As shown in the figures, the ruleis conveniently provided with an inclined scale surface 94 upon whichthere is provided a degree scale 96 conveniently marked in degrees inboth directions from a zero mark at the center of the rule. Ordinarily arule providing for a scale of 70 on either side of the center will be ofsufficient length.

Figs. '12 and 13 show in plan and elevation, respectively, a protractorindicated generally at 98 and having a concave spherically curvedundersurface 100 of the same radiusas the surface 6 of the plotting bodyIt. The protractor carries at its margin a degree scale In 2,, aroundthe sharp outer edge of the protractor.

Figs. 14 and 15 show in plan and elevation, respectively, a plottingvinstrument indicated generally at I04, the und'ersurface Hi6 of whichis spherically concave on the same radius as that of the surface of theplotting body. A sharp edge 38 .of the instrument coincides with theline of intersection between surface 106 and a diametral plane passingthrough the center for the radius of the surface I06. A bevelled "face.I I0 is provided with a degree scale H2.

Figs. 16 and 17 illustrate a-shi'eld conveniently usable with theplotting bodylD. This shield. indicated generally at I I4, is oftransparent material and its undersurface is concavely spherical to theradius of the plotting body 10. One of thesurfaces of the shield,preferably the inner surface, is conveniently marked by etching orotherwise with lines H5 corresponding to degrees of longitude and lines1 l8 corresponding to degree of latitude. The surface extent of theshield may vary. Ordinarily a shield of the dimensions approximately asshown, encompassing 45 of longitude and 70 of latitude from a diametralline representative of the equator, will be suificient.

The material or materials of which the plotting body and the severalinstruments which have been described may vary widely. The followingconsiderations should, however, be taken into account if the mostaccurate results-are to be obtained. Rigidity of the meridian member I4and the rule or compass 46 is essential for accurate work. The greatcircle rule 88 also should be rigid but it is to be noted that thisinstrument as well as other instruments to be applied to the surface ofthe plotting body when in use, obtain guidance from the surface withwhich they are in contact which tends to hold them in their trueposition. In other words, if they should be flexed slightly, contactwith the surface of the plotting body will tend to restore them to theirtrue shape. On the other hand, the elements I 4 and M receive no suchguidance. Lightn-ess of the materials used is a matter of convenience;more important is the matter of coefficient of expansion. Preferably,materials having low coeflicient of expansion are employed and in so faras is practically possible the choice of materials should be such as toprovide the minimum in difference of coefiicient of expansion betweenthe several instruments used. It is to correct for errors due todifference of expansion and the like that the marking element 52 on therule of compass 44 is adjustably mounted so that truly accuratedistancesmay be measured by this instrument on the surface of theplotting body.

The instrumentalities which have been described are useful for a widevariety of navigational and other purposes aimed at locating thegeographical position of an observer from celestial observation, and wewill first describe a procedure for locating the geographical positionof an observer by what may be termed the two star system.

As is well known to all acquainted with the art of navigation, there isa group of stars commonly known as the useful stars, the geographical orsubstellar positions of which have been carefully determined andtabulated in the nautical almanac. From the data thus available andwithout calculation, an observer is enabled by the useof our inventionto readily fix his geographical p0:

altitudes of two appropriately chosen of the usable stars, coupled withthe data available in his almanac. This may be accomplished in thefollowing simple manner, reference being had more particularly to thediagram of Fig. 18. In this diagram, is represents the sphericallycurved plotting body upon which an equator line H is plotted. A point 15on the equator line H is located to represent the intersection with theequator of the Greenwich meridian :3. These lines may, as previouslynoted, be permanently indicated on the surface of the plotting body withthe degrees of longitude indicated on the equator line. From his almanacthe observer obtains the Greenwich hour angle of the selected stars,which for convenience may be designated as stars A and B.v This datagives the observer the longitudes of the substellar positions of therespective stars at the given time and by means of the pivoted longituderule the lines of longitude of the substellar positions of therespective stars may be plotted on the plotting body. From thedeclinations given in the almanac the geographical positions of the twostars on their respective lines of longitude may then be set oh by meansof the arcuate rule, the slide on which is set to correspond with therespective declinations. For checking the accuracy of the arcuate ruleit may be conveniently placed on the equator line of the plotting body,assuming the latter to have marked thereon an accurate longitude scale.Any inaccuracy shown by such a check may readily be compensated for byadjustment of the adjustably mounted marking instrument. With the properdeclination set ofi on the arcuate rule and with the scribing point ofthe rule located at the intersection of the equator line and the properline of longitude of the substellar position of the star to be used, anarc is struck so as to intersect that line or" longitude to determine onthe surface of the plotting body the geographical position of the starto be used. In the present example, let it be assumed that the line iii! represents the Hour Circle of star A at the time of observation, andthat the line it represents the arc corresponding to the declination ofthe star. The geographical position or" the star A on the surface of theplotting body is represented by point 2|. Similarly, if line 23 is themeridian of the substellar position of the star 13 and line 25corresponds to the declination of star B, the geographical position ofthe latter is determined by point 21 on the plotting surface. While inthe interests of the greatest accuracy, the arcuate compass isadvantageously employed for laying off distances corresponding todeclinations, since this compass can readily be checked and adjustedfrom time to time for accuracy, the declinations also may be laid off bysetting to proper position the slide member 34 on the pivoted longituderule attached to the plotting body, this rule being convenientlyprovided on its longitude determining face with a suitable degree scale.

The geographical positions of the stars A and B having been determinedfor the time of observation, the altitudes of these stars are thenobserved and noted by the observer, such observations being made in asrapid succession as is consistent with accuracy. It is to be noted inthis connection that variable altitude of the observer above the surfaceof the earth does not introduce any error, the reason for this beingthat because ofthe distance to the source of light observed, th lightrays are approximately parallel. Con- 8h sequently no element of error.is introduced regardless of whether the observer be on the ground or inan aircraft in the stratosphere. From the observed altitude of star Athe zenith distance of the observer from thatstar, which is equal tominus the observed altitude, is laid off on the arcuate rule and withthe scribing point set on the geographical position 19 of the star onthe plotting surface, an'arc 29 is struck by the marking point 52, thisarc being the portion of the circle of position of the observer relativeto the geographical position of the star. Similarly, the zenith distanceof the observer from star B (90 minus the observed altitude) is set offon the arcuate rule and with point 27 as a center a second arc 3! isstruck. The intersection of the two arcs at point 33 is the geographicalposition of the observer and the latitude and longitude of this positionare readily obtainable by use of the pivoted longitude rule, assuming alongitudev scale to be applied to the plotting body, and by means of theslide carried by the longitude rule and the longitude scale associatedtherewith. Alternatively, for reasons of accuracy previously noted, thelongitudinal rule may be used merely to project the longitude line 35 ofpoint 33 to the equator and the latitude of point 33 measured along line35 by means of the arcuate rule with its vernier scale. Similarly, thesame instrument may be used to determine the longitude by measurementfrom point 3? on the equator to the point it at the intersection of theequator with the Greenwich meridian. Also for quick determination ofapproximate longitude and latitude of point 33 or similar point theshield shown in Figs. 16 and 17 may be conveniently used, the shieldbeing laid on the plotting body with the great circle or equator edge ofthe shield coincident with the equator line on the plotting body.

While it has been stated above that the intersection of the arcs 23 and3| and point 33 is representative of the position of the observer it isto be noted that these arcs if extended will intersect at a second point39 and an observer geographically located at point 33 and observing thesame stars at the same time would observe the same altitudes. It is thustheoretically possible for the observer to be either at the point 33 orpoint 39, but for all practical purposes the observer will fromextraneous factors know which one of the two theoreticallypossiblepositions he is actually occupying.

From the above, it will be clear that the result is obtained withsubstantially no calculation and also that the result is one whichobviously can.

be arrived at in an exceedingly short time after observations are made.Also, the procedure is visually accomplished and is so simple that thechances for error are minimized. The accuracy with which positions maybe determined is primarily dependent upon the accuracy with which theobservations of the stars are taken and the precision of manufacture ofthe instruments used. We have determined, however, from actualexperiment, that even with relatively very crude instruments, from whicha degree of accuracy comparable to that obtainable with precisioninstruments could not be expected, a fix or determination of theobserver's position is obtainable which is within a matter of a very fewmiles of the exact position obtained by careful and accurate computationfrom the best available data. As previously noted, we have found a scaleof 3 millimeters per degree of arc to be advantageous since such a scaleresults in a plot ting body not too large to be readily usable inrelatively cramped quarters and the scale further is readily subdividedto provide for the measurement or minutes of arc. Thus by using aVernier having a relation to the main scale of the arouate rule orcompass of 20 divisions to IE), the Vernier can be employed to anaccuracy of one minute of arc. Obviously, if a larger scale is employed,as may be done where space is not at a premium, even greater accuracy isexpectable.

In addition to the above noted advantages of simplicity and accuracythere; are, other very important advantages to be derived from the useof our invention, since for any particular intended use orgroup of uses,data on the plotting body may readily be prepared in advance. Thus priorto departure on a given intended flight, in the case of an aircraft, thegeographical positions of a relatively large number of the usable starsthat may advantageously be employed during the flight may-be locatedonthe plotting surface and in, connection with the choice of such starsit is to be noted that in the interests of accuracy in the fixing ofaposition, the most advantageous stars'to utilize are pairs of starswhich at the time of observation have geographical positions whichbear-as closely as possible at 90 from each other with respect to theposition of the observer. The reason for this will be apparent byinspection of Fig. 18, where the positions of the stars A and B bear atlittle more than a right angle from each other with respect to theobservers position. With stars thus relatively located with respect tothe observer, the arcs of the circles of position will intersect at anangle approximating a right angle and thus will give a sharply definedpoint of intersection. This obviously would not be the case were thecircles of position to intersect at an acute angle, having in mind; thevery small scale of the plotting body and a certain irreducible minimumwidth of the lines marking the circles of position.

Having beforehand a plotting body with the geographical positions of theusable stars plotted therein for times corresponding totimes during theintended flight it is very readily possible for a navigator by visualinspection of the plotting surface to determine which of the stars maymost advantageously be used at given times during the flight. Forflights scheduled in advance, all of the data necessary for the use ofgiven stars at given times can readily be worked out in advance by adispatcher from a master plotting surface, who can then instruct thenavigator what commencement of the fiight as to exactly what stars toobserve at given hours during his flight, and their coordinates, inorder to check his actual position relative to his intended position atany time during the flight.

Since the stars are moving and since there must necessarily be someelapsed time between the time it is possible to observe the altitude oftwo diiierent stars, there is introduced a theoretical margin of error,due to the fact that the georaphical positions of the stars are plottedon the plotting surface for the same instant of time and there is aslight difference in the times of actual observations of the stars. Thisin general is handled by interpolation of times of observation tocoincide with time-geographical positions of the stars.

n the other hand should we, as we now can do, select from ourdispatchers master plotting body two stars at proper altitude and atapproximately 90 from each other with respect to the 10 observersposition, of which one is transiting, that is, moving exceedingly slowlyin change, of Hour Angle and the other is rising, this error is so smallas to be negligible, being within the limits of error made inobservation of altitude because of the human equation. Even if due tosome unforeseen circumstance there should be a time interval of seriousproportions, in taking the observations of two stars for determiningthis kind of fix, this would not be serious for the reason that due tothe simplicity and rapidity with which fixes may be obtained by thepresent system, numerous observations at relatively short time intervalscan readily be taken by a navigator in flight for the purpose ofplotting'his course from a multiplicity of points which will serve tomutually check and correct each other.

The method above described, being dependent upon the observation of twocelestial bodies, is, except under exceptionally rare circumstances whenboth the sun and the moon or a planet are visible at the same time,usable only between sunset and sunrise or in other words during thosehours when thestars and planets are visible.

Our invention is not, however, limited inits use to night observation,since it can be employed to provide navigation of highly valuablepractical accuracy and utility by methods requiring observation of onlyone celestial body, such methods enabling observation of the sun to beemployed, with consequent utility during daylight hours. One suchadditional method is fully described in our application Serial No.453,608, of which this is a division.

It is evident that many variations in the specific design of theequipment employed and variations in the specific application of themethods hereinbefore described may be made Without departing from theprinciples of the invention, the scope of which is to be understood asembracing all ieatures falling within the scope of the appended claims.

What is claimed:

1. For use in celestial navigation, a plotting body having a sphericallycurved plotting surface the radius of which bears a predetermined scalerelationship to the radius of the earth, and an independentlymanipulatable rule for selectively marking arcs of circles about centerslocated in any selected relation and position on said plotting surface,said rule comprising an arcuate body member bearing an arcuate scale anda slide member adjustable along the length of said body member, one ofsaid members carrying a pointed element projecting inwardly on a radiusof the arc of said scale adapted to engage said plotting surface at aselected place thereon to permit the rule to be swung around such placeas a center and the other of said members carrying an inwardlyprojecting marking element for marking an are on said plotting surfacewhen the rule is swung, said elements being radially adjustable tocontact the plotting surface when the arc of said scale is trulyconcentric with said plotting surface, at least one or said elementsbeing adjustably carried by one of said members for adjustment in adirection lengthwise of said body member and said marking element beingpivotally mounted to provide a lengthwise adjustment thereof.

2. An arcuate rule for use in celestial navigation with a plotting bodyhaving a spherically curved plotting surface the radius of which bears apredetermined scale relationship to the radius of the earth, said rulecomprising an arcuate body member and a slide member, said membershaving cooperatively engaging slide surfaces for permitting the slidingmember to move in an arcuate path along said body member and meansclamping the slide member in a predetermined position, said body memberhaving a supporting means comprising a radially adjustable blunt elementlocated adjacent one end of the body member and adapted to slide on theplotting surface, the body member being provided with a scale formeasuring the degrees of an are, a radially adjustable pointed elementbeing carried by the slide member for engaging the plotting surface, anda marking element being carried by the body member adjacent the otherend thereof for marking an are on the plotting surface with the pointedelement providing a center about which the arc is marked, the positionof the body member being adjusted by the supporting means and th pointedelement so that the arc thereof will be truly concentric with theplotting surface at all times.

3. A device as set forth in claim 2 in which said marking element ispivotally mounted about an axis normal to the plane of said scale topermit the adjustment thereof to a position such that the point of themarking element lies exactly on a radius struck from a predeterminedposition on said arcuate scale to the center about which the arc of thescale is struck.

4. An arcuate rule for use in celestial navigation with a plotting bodyhaving a spherically curved plotting surface the radius of which bears apredetermined scale relationshi to the radius body member adjacent toone end thereof and a radially adjustable marking element extendingREFERENCES CITED The following references are of record in the file ofthis patent:

UNITED STATES PATENTS Number Name Date 168,514 McVicar Oct. 5, 1875295,076 Svenson Mar. 11, 1884 371,160 Wylie et al Oct. 4, 1887 379,914Story Mar. 20, 1888 387,957 Moreon et a1 Aug. 14, 1888 774,998 WillsonNov. 15, 1904 844,536 Prindle Feb. 19, 1907 1,016,176 Roca Jan. 30, 19121,175,612 Cresse -4 Mar. 14, 1916 1,282,020 Anderson Oct. 22, 19181,351,941 Challet Sept. 7, 1920 1,352,320 Souders Sept. 7, 19201,392,825 Gonzales Oct. 4-, 1921 1,619,750 Nelson Mar. 1, 1927 1,826,081Magers Oct. 6, 1931 1,849,202 Pfuger Mar. 15, 1932 2,420,608 Menge May13, 1947 FOREIGN PATENTS Number Country Date 133 Great Britain Jan. 18,1860 of 1860 2.457 Great Britain May 24, 1882 of 1882 125,526 GermanySept. 20, 1901 130,930 Great Britain Aug. 14, 1919 149,293 Germany May10, 1903

